The law, which takes effect Dec. 31, would prohibit courses that promote resentment toward one race; that are designed for students of one race; that promote ethnic solidarity “instead of treating students as individuals;” and that encourage “the overthrow of the United States government.”

The proposal was the brainchild of Tom Horne, Arizona state superintendent of public instruction, who has long battled with the Tucson Unified School District over its Mexican-American studies program, contending that it promotes “ethnic chauvinism” through the use of textbooks such as “Oppressed America” and at least one guest speaker who said, “Republicans hate Latinos.”

Those who contend the law promotes racism are missing the point, Mr. Horne said.

“It’s the opposite of racism,” said the Republican, who is running for state attorney general. “We’re trying to get schools to treat students as individuals and not on the basis of race.”

Still, reaction to the law has been swift. No less than a United Nations human rights panel issued a statement the day before the law was signed, warning that it violated Arizona’s obligation to “promote a social and cultural environment conducive to respect for ethnic and cultural diversity.”

Supporters of the ethnic studies programs have argued that enrolled students perform better than their peers who don’t participate in the program. Two Oregon State University researchers released a statement Tuesday saying that the law “could negatively affect students’ academic achievement and reverse academic gains made over the last several years.”

Sean Arce, director of the Mexican-American studies department in the Tucson school district, said the district’s ethnic studies program conforms to the law’s guidelines.

“In no way do we teach the resentment of any particular group of people,” Mr. Arce told the Arizona Republic newspaper.

The new law comes amid growing aftershocks from the state’s new illegal immigration statute, which gives state and local police the right to arrest anyone reasonably suspected of being in the country illegally.

Los Angeles on Wednesday became the largest municipality to date to announce an economic boycott of Arizona over the law.

The City Council voted 13-1 to bar Los Angeles from conducting business with Arizona unless the law is repealed. Critics say the law will promote racial profiling, a charge Mrs. Brewer has dismissed as “just pure rhetoric.”

Los Angeles Mayor Antonio Villaraigosa has said he would approve the boycott, which is estimated to affect investments and contracts worth as much as $52 million.

As for the ethnic studies law, Mr. Horne said, it does nothing to prevent schools from teaching about students’ cultures.

“We should learn about different heritages and languages, and I’m all for that,” he said. “I’m just opposed to dividing students up and only teaching them about their own.”

Among the Arizona schools that could be affected by the law are three charter schools run by Chicanos Por La Causa, a nonprofit group that bills itself as the state’s largest community development corporation.

But spokeswoman Amanda Roberson said she doubted the schools would be in danger of losing funding. Schools that violate the law would lose a share of state education funds.

“We don’t think right now it’s going to apply to us,” said Ms. Roberson. “The language is very extreme - I mean, it talks about overthrowing the government - and we don’t think it applies to us.”

Mr. Horne has argued that the curriculum prods Hispanic students into believing they are oppressed by whites. He pointed to a 2006 talk by Hispanic activist Dolores Huerta, who told students, “Republicans hate Latinos.”

He also cited the use of textbooks such as “Oppressed America,” which quotes a Hispanic activist saying that Chicanos should “kill the gringo.” Another textbook, he says, “The Mexican American Heritage,” promotes the idea of Aztlan, the five Southwestern states that activists say should be returned to Mexican control.